On the minimal area of quadrangles circumscribed about planar convex bodies
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908949994799104 |
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| author | Fodor, Ferenc Grundbacher, Florian |
| author_facet | Fodor, Ferenc Grundbacher, Florian |
| contents | We show that every planar convex body is contained in a quadrangle whose area is less than $(1 - 2.6 \cdot 10^{-7}) \sqrt{2}$ times the area of the original convex body, improving the best known upper bound by W. Kuperberg. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05185 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the minimal area of quadrangles circumscribed about planar convex bodies Fodor, Ferenc Grundbacher, Florian Metric Geometry 52A27 (Primary) 52A10, 52A40 (Secondary) We show that every planar convex body is contained in a quadrangle whose area is less than $(1 - 2.6 \cdot 10^{-7}) \sqrt{2}$ times the area of the original convex body, improving the best known upper bound by W. Kuperberg. |
| title | On the minimal area of quadrangles circumscribed about planar convex bodies |
| topic | Metric Geometry 52A27 (Primary) 52A10, 52A40 (Secondary) |
| url | https://arxiv.org/abs/2506.05185 |